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Heads or Tails: An Introduction to Limit Theorems in Probability

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Emmanuel Lesigne

Everyone knows some of the basics of probability, perhaps
enough to play cards. Beyond the introductory ideas, there are many
wonderful results that are unfamiliar to the layman, but which are
well within our grasp to understand and appreciate. Some of the most
remarkable results in probability are those that are related to limit
theorems—statements about what happens when the trial is
repeated many times. The most famous of these is the Law of Large
Numbers, which mathematicians, engineers, economists, and many others
use every day.

In this book, Lesigne has made these limit theorems accessible by
stating everything in terms of a game of tossing of a coin: heads or
tails. In this way, the analysis becomes much clearer, helping
establish the reader's intuition about probability. Moreover, very
little generality is lost, as many situations can be modelled from
combinations of coin tosses.

This book is suitable for anyone who would like to learn more about
mathematical probability and has had a one-year undergraduate course
in analysis.

Readership

Undergraduates and beginning graduate students
interested in mathematical probability.

Reviews & Endorsements

This is a delightful little book ... the author converys an impressive and
well-written account of central ideas of limit theorems in probability ... It
is refreshing to have a book that starts with such a simple experiment with
two outcomes and takes us as far as it does into the world of probability
theory.

-- MAA Reviews

The proposal is very
attractive. ... (It) is helpful for the probability community to have
access to this book, which contains a unified and elementary presentation of
limit theorems...

Table of Contents

Heads or Tails: An Introduction to Limit Theorems in Probability

Title (HTML):
Heads or Tails: An Introduction to Limit Theorems in Probability

Author(s) (Product display):
Emmanuel Lesigne

Affiliation(s) (HTML):
Université François Rabelais, Tours, France

Abstract:

Everyone knows some of the basics of probability, perhaps
enough to play cards. Beyond the introductory ideas, there are many
wonderful results that are unfamiliar to the layman, but which are
well within our grasp to understand and appreciate. Some of the most
remarkable results in probability are those that are related to limit
theorems—statements about what happens when the trial is
repeated many times. The most famous of these is the Law of Large
Numbers, which mathematicians, engineers, economists, and many others
use every day.

In this book, Lesigne has made these limit theorems accessible by
stating everything in terms of a game of tossing of a coin: heads or
tails. In this way, the analysis becomes much clearer, helping
establish the reader's intuition about probability. Moreover, very
little generality is lost, as many situations can be modelled from
combinations of coin tosses.

This book is suitable for anyone who would like to learn more about
mathematical probability and has had a one-year undergraduate course
in analysis.

Undergraduates and beginning graduate students
interested in mathematical probability.

Reviews:

This is a delightful little book ... the author converys an impressive and
well-written account of central ideas of limit theorems in probability ... It
is refreshing to have a book that starts with such a simple experiment with
two outcomes and takes us as far as it does into the world of probability
theory.

-- MAA Reviews

The proposal is very
attractive. ... (It) is helpful for the probability community to have
access to this book, which contains a unified and elementary presentation of
limit theorems...